No Time to Try puzzle in Mathematica.

From https://twitter.com/robeastaway/status/1447627451874545665
“””
A cracking James Blond puzzle by @stecks in this week’s New Scientist

    Puzzle 
    set by Katie Steckles
    #134 No time to try 

    James Blond edges along the corridors of the super villan’s base, and 
    comes to two locked doors, each with a keypad that requires a four-digit
    code. He will need to get through one of the door, but there is no time
    to guess a four-digit code - the number of possible combinations is 
    staggering. 

    But wait! Some of the buttons on the keypads are visible worn down,
    while others look as if they have never been pressed.

      [ 
         Left: 1,5,6,0 is worn down     Right: 2,6,7 is worn down. 
      ]

    One door has a keypad with four worn buttons, the other has three.
    Blond only has time to try one door, and he will have to try all
    the possible combinations.

    Which of the two keypads will give him fewer combinations to try - 
    the one with four worn buttons, or the one with three?
“””

Print["Left:",Permutations[{1,5,6,0}]//Length]
Print["Right:", Flatten[Permutations[Flatten@{#,right}]&/@(right={2,6,7}),1]//Length]